Abstract: Ideally, Atwood’s Machine consists of two masses, connected by a massless inelastic string threaded over a frictionless pulley. In this experiment, the dependence of the acceleration on the two masses was investigated.
Atwood’s Machine is represented schematically to the left. Upon inspection, Newton’s Second Law for the system can be derived:
For m1: (1)
For m2: (2)
Solving the (1) for N, followed by substitution into (2), yields the following equation:
Rearranging terms and solving for a:
By using the photogate and the LoggerPro software, the acceleration of the system may be determined, as well as the dependence on the masses.
A series of masses were placed on either side of the pulley, released from rest and allowed to accelerate a distance of at least 40 cm. The velocity of the system was plotted vs. time, the acceleration determined from the slope of the least-squares line. Initially, the total mass in the system was kept constant, beginning with 200 grams on each side. After each trial, 20 grams from one side was transferred to the other. For the second part of the experiment, the difference between the two masses was kept at a constant 20 grams, adding an equal amount of mass to each side.
Necessary Equipment: Windows PC, LabPro Interface, Logger Pro software, Vernier Photogate, Super Pulley, mass set, string. All materials provided by the Bemidji State University Department of Physics.
As can be seen from the chart to the left, the acceleration is proportional to the difference between the two masses, as predicted from equation (3). Also shown on the chart is the predicted acceleration, calculated from (3); note that they are both proportional, and differ only a constant.
Part I| | | Part II| | |
a, calc, m/s2| a, exp, m/s2| % Diff| a, calc, m/s2| a, exp, m/s2| % Diff| 0| 0| n/a| 0.892| 0.821| 8.0|...